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Frailty Models Under Xgamma Distribution with Application to Survival Data

Frailty models provide an alternative to proportional hazards models, which are designed to discover the properties of the unobserved heterogeneity in individual risks of disease and death. In spite of this distribution of the frailty is normally assumed to be continuous. In some circumstances, it is appropriate to recollect discrete frailty distributions. Generally, Gamma, Weibull, Exponential, Lognormal, and Log-logistic baseline distributions have fitted with frailty distribution. The Xgamma distribution among a unique finite aggregate of exponential and gamma distribution and allowance for the different shapes of the hazard function. The study aims to fit the above four distributions with the Xgamma baseline distribution and apply them to test popular actual-lifestyles statistics set. The study result revealed that Xgamma with Positive Stable (PS) frailty model is a good choice for the Veterans' Administration Lung Cancer study data set and Xgamma with Log-Normal (LN) frailty model is the best fit for the Culling dairy heifer cow’s data set. Additionally, Xgamma identifies the baseline distribution with the lowest Akaike's Information Criteria (AIC) and Bayesian Information Criteria (BIC) values. The study result proved Xgamma distribution and its extended model for frailty distribution is the possible approach in a real-life time or survival analysis.

Xgamma Distribution, Hazard Function, Survival Analysis, Parametric Frailty Models, Marginal LOG-Likelihood, Clustered Data Analysis

Ashok Kumar Palanisamy, Muthukumar Madaswamy. (2023). Frailty Models Under Xgamma Distribution with Application to Survival Data. Mathematics and Computer Science, 8(4), 87-93.

Copyright © 2023 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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